Iterative learning algorithms for boundary tracing of fractional diffusion equations

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作   者：

Wang, Jungang;  Wang, Qian;  Bao, Jun;  Si, Qingyang; 

作者机构：

Northwestern Polytechnical University School of Mathematics and Statistics; 

关键词：

convergence analysis;  iterative learning control;  fractional diffusion equation;  SYSTEMS;  boundary control; 

期刊名称：

Asian Journal of Control: Affiliated with ACPA, the Asian Control Professors Association

i s s n：

1561-8625

年卷期：

2024 年 26 卷 1 期

页   码：

190-204

页   码：

摘   要：

We study P-type and PI & theta;$$ {} circumflex {theta } $$-type iterative learning control (ILC) schemes for boundary tracing problem of nonhomogeneous fractional diffusion equations. Based on Sobolev imbedding theorem, we derive sufficient conditions for the convergence of four ILC schemes in the sense of & lambda;$$ lambda $$-norm. Numerical examples are presented to illustrate effectiveness of the proposed control methods. The results show that closed-loop ILC scheme converges faster than open-loop ILC scheme; moreover, PI & theta;$$ {} circumflex {theta } $$-type (0.5<& theta;<1)$$ left(0.5<1right) $$ ILC scheme outperforms P-type and PI-type (& theta;=1)$$ left(theta equal to 1right) $$ ILC schemes in terms of the convergence speed.